In all seriousness how feasible is it to run a hot air gun over the TPM chip and remove it before even you first boot the computer? Would the computer boot? And if it does, would it just go with "Oh, I thought I came equipped with a TPM chip. I don't seem to have one. Oh well, let's carry on anyway"?

I would suspect that depends on the datasheet of the chip and if there's any check mechanisms in the UEFI.

It could be implemented in such a way that removing it would cause problems but it shouldn't be too hard to work around it.

Worst case you would you would replace it with something that imitates its response when the UEFI searches for it.

Since a lot of motherboards have spaces for it but seem to function just fine without it leads me to believe it should work just by removing it.